What are the length of the side of a cube and the volume if the mass of the cube is 50g?the density of the material of cube is 7.8g/cm^3

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The density of an object is given by density = mass/volume.

Let the side of the cube be S.

The volume of a cube of side S = S^3

The mass is 50 g and density is 7.8 g/cm^3

Using the information provided we can create an equation:

7.8 = 50/S^3

=> S^3 = 50/7.8 = 6.410 cm^3

The volume of the cube is 6.41 cm^3

S = (50/7.8)^(1/3) = 1.857 cm

The length of the side of the cube is 1.857 cm and the volume is 6.41 cm^3.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since to determine the length of each side of the cube, we need to know the volume, we'll begin by calculating the volume.

First, we'll recall the volume formula:

V = mass/density

From enunciation, we know the mass and the density of material, therefore we can calculate the volume of the cube:

V = 50 g/7.8 g/cm^3

V = 6.410 cm^3

We'll recall the formula that gives the volume of a cube:

V = l^3, where l is the length of the side of the cube.

6.410 = l^3

l = cube root (6.410)

l = 1.857 cm

The requested length of the side of the cube and the volume of the cube are: l = 1.857 cm and V = 6.410 cm^3.

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